Dynamics of a Lattice Gauge Theory with Fermionic Matter -- Minimal Quantum Simulator with Time-Dependent Impurities in Ultracold Gases

TL;DR

This paper introduces a minimal model for simulating the real-time dynamics of a $\

Contribution

It presents a novel approach to implement and measure a $\

Findings

Dynamical correlators of gauge fields can be experimentally measured.

The model reveals unexpected features in the integrable limit.

Potential for simulating strongly-interacting lattice gauge theories.

Abstract

We propose a minimal model to study the real-time dynamics of a $\mathbb{Z}_2$ lattice gauge theory coupled to fermionic matter in a cold atom quantum simulator setup. We show that dynamical correlators of the gauge fields can be measured in experiments studying the time-evolution of two pairs of impurities, and suggest the protocol for implementing the model in cold atom experiments. Further, we discuss a number of unexpected features found in the integrable limit of the model, as well as its extensions to a non-integrable case. A potential experimental implementation of our model in the latter regime would allow one to simulate strongly-interacting lattice gauge theories beyond current capabilities of classical computers.